The present invention relates to an electrical connection device for conducting cable shields, in particular those of telecommunication cables. This invention applies more particularly to cables provided with a protective shield of very small thickness, consisting of a metal layer, especially an aluminum layer, covered with an insulating protective layer, such as one made of polyethylene. Such a shield, together with its connection device, makes it possible to protect the cable which it surrounds from radiofrequency electromagnetic interference and to provide grounding or connection to a chassis, for example by connecting a cable, forming part of an installation, to a structure receiving this installation, or to provide continuity between two shields.